By Oregon State University, 1977 Symposium in Pure Mathematics

ISBN-10: 0821814354

ISBN-13: 9780821814352

ISBN-10: 0821814370

ISBN-13: 9780821814376

ISBN-10: 0821814745

ISBN-13: 9780821814741

ISBN-10: 2219752372

ISBN-13: 9782219752376

ISBN-10: 4019771952

ISBN-13: 9784019771953

ISBN-10: 9419746496

ISBN-13: 9789419746495

Includes sections on Automorphic representations and L-functions in addition to Arithmetical algebraic geometry and L-functions

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**Additional resources for Automorphic Forms, Representations and L-Functions, Part 2**

**Example text**

19A T H E O R E M ( S P E C K E R is free for any cardinal a. [50]-N6BELING [68]). 4. 19B T H E O R E M Hom(Za,Z)is free. (SPECKER [50]-BALCERZYK [62]). g. , any subgroup A with \A\ < tti is free. 20. Dubois' Theorem. Let P(R) = Ru denote the set of all countable sequences of elements of R and B(R) those sequences such that the entries form a finite set. B{Z) is the set of all bounded sequences in P(Z). For cardinals m and mi, let m = mi mean either both are finite or both are equal. 19A to rings but restricted to a = to.

The torsion subgroup t(R) of the additive group of a ring R is an ideal of R. If t(R) is a ring direct factor of i2, then R is said to be fissile. 28. 26A T H E O R E M (T. S Z E L E - L . FUCHS [56], C. AYOUB [77], AND D. V. HUYNH [77]). / / a ring R satisfies the dec on principal right ideals, then R is fissile; in fact, there is a unique ideal I such that R = T x I, where T = t(R). REMARK. A ring R satisfying the dec on principal right ideals is called left perfect. 31. , while those of Ayoub and Huynh are for perfect rings.

16. Corner's Theorem and the Dugas-Gobel Theorem. 16 CORNER'S T H E O R E M [63]. Every countable ring A whose additive group is reduced and torsionfree is isomorphic to the endomorphism ring of an Abelian group with the same properties. An Abelian group A has no nonzero cotorsion subgroups if A is reduced, torsionfree, and has no subgroup ~ ^( p ), the group of p-adic integers, for any prime p. In this case, A is said to be cotorsion-free. A ring R is cotorsion-free if its additive group is cotorsion-free.

### Automorphic Forms, Representations and L-Functions, Part 2 by Oregon State University, 1977 Symposium in Pure Mathematics

by Christopher

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